Q - Leap Strike - Leap Strike is very helpful with either a) ganking from the bushes or b)finishing off a runner.
W - Empower - Empower is a very helpful spell and is great for combo attack with leap strike. If you do leap strike make sure to press w before striking so it does a lot more damage
E - Counter Strike - Counter Strike is where Jax stuns surrounding enemies and makes them immobile very useful especially with nija tabi because it helps you dodge and you cant use counter strike unless you just dodged an attack. It is great for ganking because it doesn't let them get away.
R - Jax's Ult really just enhances your attack damage so use it when youre in a big fight

Why i got...
Flash - Because flash is great for chasing down runners if you use flash AND leap strike you can finish off practically any runner there is.
Teleport - It's very useful for counter pushes. If someone pushes your turret, teleport there. empower/leap strike combo, counter strike. their done for. then you push their turret

Guinsoo's - Guinsoos is very helful as it helps your damage and ap and attack spped
Phantom Dancer - Phantomdancer is VERY helpful because with all of the attack damage you want to be able to hit them as many times as possible, and its great for minion/turret killing
Mordred's/Infinity Edge - you need the damage
2nd infinity edge- you dont really need this, im a fan of it though just because i like hitting really hard